Matt Fagerson was sent off late in the game

Fraser Brown opened the scoring for Warriors after the home pack went over from a driving maul but La Rochelle, despite having nothing to play for, went ahead with scores from Jules Favre and Levani Botia.

In a scoreless second-half, Scott Cummings' last-minute try was disallowed when Matt Fagerson was judged to have led with his forearm in the build-up.

That would have brought Glasgow level with a conversion to come, but instead Fagerson was shown a red card.

The loss leaves them five points behind pool three leaders Exeter Chiefs, who face Sale on Sunday, and with little hope of taking one of three best runners-up spots.

"It's tough from here, no doubt," said Rennie after the Scotstoun setback.

"We'll need to beat Exeter with a bonus (point) and probably need to get five [points] out of Sale.

"The way a couple of groups are looking you going to need some big numbers to get through if you don't win your pool. Probably 19 (points) or so. It's not terminal but it's tougher from here.

"We had all the ball and all the territory in the second half and couldn't get over the line," Rennie said. "Some of it was decision-making and a bit of patience.

"They constantly infringed down there. We had plenty of chances to put them away we just need to be more accurate."